Chapter 6 - Probability
Chapter 6 Practice
1. Two identical spinners each have five equal sectors that are numbered 1 to 5. What is
the probability of a total of 7 when you spin both these spinners?
P A  
4
25
2. Tom is practicing archery with a target that has three concentric zones: a circular
bull’s-eye in the centre, an inner ring, and an outer ring. He has a 0.12 probability of
hitting the bull’s-eye, a 0.37 probability of hitting the inner ring, and a 0.43 probability
of hitting the outer ring. On an given shot, what is the probability that Tom
a) Misses the target?
b) Hits the target but does not get a bull’s-eye?
c) Hits the inner ring or the bull’s-eye?
a) P A   1  0.12  0.37  0.43
 0.08
b) P A   0.37  0.43
 0.8
c) P A  B   0.12  0.37
 0.49
3. The probability of Jim hitting the bull’s-eye on a dart board is 0.04. What are the odds
in favour of Jim not hitting the bull’s-eye?
Odds in favour 
0.04
 1 : 24
0.96
4. What are the odds in favour of a total greater than 9 in a given roll of two standard
dice?
Odds in favour 
6
36
30
1:5
36
5. If a bowl contains ten hazelnuts and eight almonds, what is the probability that four
nuts randomly selected from the bowl will all be hazelnuts?
P A  
C4
210
7


 0.0686
3060 102
18 C4
10
6. If a CD player is programmed to play the CD tracks in random order, what is the
probability that it will play six songs from a CD in order from your favourite to your
least favourite?
P A  
1
1

0.001389
6! 720
7. A six-member working group to plan a student common room is to be selected from five
teachers and nine students. If the working group is randomly selected, what is the
probability that it will include at least two teachers?
Case of no teachers:
P A  
C6
84
4


 0.028
C
3003
143
14 6
Case of 1 teacher:
P A  
5
9
C1  9 C5
630
30


 0.2098
3003 143
14 C6
Probability of at least two teachers:
P A   1  0.028  0.2098
 0.7622
8. Leela has five white and six grey huskies in her kennel. If a wilderness expedition
chooses a team of six sled dogs at random from Leela’s kennel, what is the probability
the team will consist of
a) Exactly two white huskies?
b) All grey huskies?
c) Three of each colour?
a) P A  
5
c) P A  
5
C2  6 C4 150 25


 0.3247
462 77
11 C6
b) P A  
C6
1

 0.00216
462
11 C6
6
C3  6 C3 200 100


 0.4329
462 231
11 C6
9. Suppose you simultaneously roll a standard die and spin a spinner that is divided into 10
equal sectors, numbered 1 to 10. What is the probability of getting a 4 on both the die
and the spinner?
P  A  B   P  A   P B  
1 1
1
 
10 6 60
10. Carrie is a kicker on her rugby team. She estimates that her chances of scoring on a
penalty kick during a game are 75% when there is no wind, but only 60% on a windy day.
If the weather forecast gives a 55% probability of windy weather today, what is the
probability of Carrie scoring on a penalty kick in a match this afternoon?
Windy and Score: P A  B   P (A)  P (B A)  0.55  0.6  0.33
Not Windy and Score: P A  B   P (A)  P (B A)  0.45  0.75   0.3375
P(Scoring) = (Windy and score) OR (Not Windy and score)  0.33  0.3375  0.6675
11. If 28% of the population of Statsville wears contact lenses, 37% have blue eyes, and
9% are blue-eyed people who wear contact lenses, what is the probability that a
randomly selected resident has neither blue eyes nor contact lenses?
P(Blue Eyes OR Contacts) = P B  C
  P (B )  P (C )  P (B  C )
 0.37  0.28  0.09
 0.56
P(NOT Blue Eyes OR Contacts)
 1  0.56
 0.44
12. Steve estimates that he has a 65% chance of passing Math and a 70% chance of
passing English. Assuming that Math and English are independent events,
a) What is the probability that Steve will pass Math but fail English?
b) What is the probability that Steve fails both subjects?
c) What is the probability that Steve passes both subjects?
a) P  M  E '  P M   P E '  0.65  0.3  0.195
b) P  M ' E '  0.35  0.3  0.105
c) P  M  E   0.65  0.7   0.455